Every day is a mental maths day

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AT1 Making maths real for children

• Liz Thomas Teaching and Learning Adviser
  (Numeracy and Assessment)
• Mel Willcox Teaching and Learning Consultant
  KS1 (CLLD/Numeracy)
• Sue Lock - AST

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Course objectives

• Be familiar with the progression in Using and
  Applying
• Have a range of teaching strategies to make
  maths real for children
• Be able to assess pupil skills in using and
  applying

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Why make maths real?
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Obstacles to progress in mathematics

• Too often pupils are expected to remember
  methods, rules and facts without grasping the
  underpinning concepts, making connections with
  earlier learning and making sense of the
  mathematics so that they can use it independently
• Ofsted Understanding the score report 2008

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Independent Review of the Primary Curriculum
Final Report

• Talking mathematics should extend to high
  quality discussion of mathematical investigations
  that develop childrens logical reasoning and
  deduction, which underpin mathematical thinking
  .
• The ultimate goal is to develop mathematical
  understanding i.e. comprehension of mathematical
  ideas and applications.

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which means

• Children become at home with number so as to
  be able to apply number knowledge and skills
  effortlessly in order to understand and seek
  solutions to challenging mathematical problems.

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However

• Lack of opportunities to apply and use
  mathematics, which leads to children not
  understanding what to do when faced with real
  life mathematical problems
• Independent Review of Mathematics Teaching in
  Early Years Settings and Primary Schools Sir
  Peter Williams June 2008 Mathematics
  Understanding the Score OFSTED September 2008

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Agenda

• Progression in Using and Applying
• Number activities
• Supporting Using applying
• Resources
• Shape, Space Measure activities
• Supporting Using applying
• Resources
• Assessing Using and Applying

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Help Noah . . . .

• Noah saw twelve legs go into the ark, how many
  creatures did he see?

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Progression in Using and Applying

• What strategies did you use to solve the problem?
• What strategies might children use to solve the
  problem?

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Some childrens solutions
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Some childrens solutions 2

• Three kangaroos and a turtle
• Fred from Wylde Green School wrote
• three animals with 4 legs or six animals with
  2 legs or one with 4 legs and four with 2
  legs or two with 4 legs and two with 2 legs

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Using Applying
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What does each of these assessment headings mean
to you ?

• Problem solving
• Reasoning
• Communicating

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APP Bingo

• Work as a table
• Sort the cards into the three strands for using
  applying
• Problem solving
• Reasoning
• Communication

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Progression of the strands

• Problem solving
• Reasoning
• Communicating
• What does it look like in year groups ?

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Problem Solving
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Reasoning / Communicating

• Modelling talk
• Modelling systematic recording
• Modelling logical thinking
• Discussion
• What do these look like in the classroom ?

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Coffee / Tea
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Obstacles to progress in mathematics 2

• In number and calculation, pupils
• have difficulty in identifying related facts from
  known number facts
• were reluctant to use their mental calculation
  skills
• used formal written methods in preference to
  mental methods as the believed formal methods
  were better
• the children were weak on mental calculation.
  They had few strategies and relied heavily on
  counting on and back, often making mistakes
• the targeted children rarely looked at a
  calculation to decide whether to do it mentally
  or to use a written method
• Keeping up Pupils who fall behind in KS2

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Young children can solve mathematical problems
for which they dont have formal techniques if
the problems are presented in a meaningfully way.

• Ask a six year old what 3 divide by 4 isat best
  they will tell you its impossiblebut if you
  offer that same six year old 3 bars of chocolate
  and ask then to share between four friends she
  will try it!!!!

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Mystery Numbers

• I am thinking of a number. It can be divided
  exactly by 3. If I divide it by 2,4 5 there is a
  remainder of 1.
• Find one number to fit the puzzle that is less
  than 30.
• Find one number to fit the puzzle that is greater
  than 50 and less than 100.

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Even Boats
12 children want to cross a river. There are 3
boats.
All boats have to cross the river at the same
time. Each boat must carry an even number of
children.
How many ways can the boats cross the river?
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Skipping Rope Puzzle

• Some children wanted to skip together, so they
  found a
• long rope. But half of it was rotten, so they cut
  off half and threw it away. The rope was still
  too long, so they cut off a third more. They used
  the rest of the rope for skipping.
• The rope was 18m long to start with.
• How long was the skipping rope ?
• What if they started with 24m?
• How long would their skipping rope be ?

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This activity is based on a very simple idea of
scoring points by throwing beanbags at a
target. Throw 3 beanbags at the target. The total
number of points scored is the sum of the numbers
where the beanbags land.
What is the smallest total that can be made with
3 beanbags? What is the next smallest total
that can be made with 3 beanbags? What is the
largest total that can be made with 3 beanbags?
Look at the first 2 calculations for the smallest
and second smallest totals. What do you think is
the next largest total that can be made with 3
beanbags?
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Problem Solving
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Time to explore

• House prices
• The Dino Diner
• Queen Hatshepsut
• The Birthday Party

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Money box

• Jian empties his money box.
• There are 12 coins.
• ¼ are 10p coins.
• Another ¼ are 50p coins.
• He has two 1 coins and two 2 coins.
• The rest are 5p coins.
• How much does he have ?

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Class Trip

• Imagine a class are going on a trip. There are 32
  pupils in the class. They plan to go in 4 groups.
  How many in each group?
• What if they get into 5 groups?
• What if there are only 28 children?
• At the theme park an adults price is 12.00 A
  childs entry is half of this- how much for a
  child?
• How much is the price for a toddler of less than
  2 if this is half of the childs price?
• You can buy a group ticket for 1 adult and 3
  children for 20.00. How much cheaper is this
  overall?

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Lunchtime
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Obstacles to Shape and Space

• As a table discuss what are obstacles for pupils
  accessing shape and space activities ?

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Pentagon Problem
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Sorting Cards- 2D Shape Problem You have 9 clues

• The shapes are arranged in a row like this
• Shape 3 has 1 side
• The triangle is shape number 1
• You need 5 shapes a circle, a triangle, a
  rectangle, a square and a pentagon
• Shape number 5 has the most sides
• The rectangle and square are not next to each
  other
• Shapes 2 and 4 have 4 sides
• Shape 2 has 4 sides the same length
• A pentagon has 5 sides

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Do you measure up ?

• I think your height is eight times the distance
  from the top of your head to your chin. Do you
  think this is true? How can we find out?
• Investigate other body measures e.g. Is your
  thumb the same length as your nose? Is your foot
  the same length as the distance from your wrist
  to your elbow?

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Cooking for many !!

• In a chosen recipe you might ask the children to
  consider if it would matter if they didn't all
  use exactly the same amounts used in this recipe?
  
• What about if they were baking a cake? or making
  a spaghetti sauce?

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Walking on the moon

• You could talk to the children about how
  gravity on Earth affects how much we weigh and
  introduce the idea that gravity is different on
  other planets in our Solar System.
• If it is available, you could show video
  images of astronauts on the surface of the moon
  showing them carrying large objects and being
  able to jump very high because of the reduced
  gravity.
• Using a website the children could enter
  their weight on Earth and to see how much they
  would weigh on the other planets. You might ask
  them to predict whether they think they will be
  heavier or lighter on each planet and ask them to
  give reasons for their predictions

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Time to explore

• Egyptian Area and Perimeter
• Dyno park fun
• Cartwheel problem
• Victorian garden
• Egyptian Weight
• Pattern

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Coffee / Tea
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Making maths Real

• Teachers TV
• Discussion

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Assessing Using and Applying

• A look at some childrens work - one task
  whole school
• Other examples Standards Files

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Resources

• Stick..\..\app 2009-10\draft_sotm.zip on Maths
  and levelopaedia
• Websites learningwithsouthglos
• Process and Context Mapped to Framework (
  Curriculum maps - nrich)
• Cornwall Contexts